The AU task was introduced by Couvreur et
al. [1]} as a fundamental primitive for
asynchronous systems.
Shortly after, Awerbuch et al. [2]} observed that this
task captures the essence of constructing a self-stabilizing synchronizer and
developed a self-stabilizing anonymous size-uniform AU algorithm that
stabilizes in
\(O (D)\) 
time, albeit with an unbounded state space.
By incorporating a reset module into their algorithm, Awerbuch et al. obtained a self-stabilizing AU algorithm with a bounded state space and the
same asymptotic stabilization time, however, the reset module requires unique
node IDs and/or the knowledge of \(n\)  (or an approximation thereof), which
means in particular that its state space is
\(\Omega (\log n)\) ;
it also relies on unicast communication.
